Subgroups — C₃×C₅×#3311 #14276345

Order 1920.

804 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3311	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#126	—	2	1	no	—
26	C₃×C₅×#126	—	2	1	no	—
27	C₃×C₅×#124	—	2	1	no	—
28	C₃×C₅×#124	C₂²	1	1	yes	characteristic
29	C₃×C₅×#123	—	2	1	no	—
30	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#121	—	2	1	no	—
34	C₃×C₅×#121	C₂²	1	1	yes	characteristic
35	C₃×C₅×#120	—	2	1	no	—
36	C₃×C₄×C₅×Q₈	—	2	1	no	—
37	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₃×C₅×#117	C₂²	1	1	yes	characteristic
41	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
43	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×#102	C₂²	1	1	yes	characteristic
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic
54	C₃×C₅×#102	C₂²	1	1	yes	characteristic
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic
56	C₃×C₅×#102	C₂²	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3311	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#546	C₂×C₃	1	1	yes	characteristic
63	C₅×#489	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#485	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#482	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#470	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#465	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#464	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#450	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#440	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#435	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#418	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂⁴×C₃×C₅	—	2	1	no	—
77	C₃×C₅×#41	—	2	2	no	—
78	C₃×C₅×#41	—	4	1	no	—
79	C₂×C₃×C₅×Q₈	—	2	1	no	—
80	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	—	2	2	no	—
83	C₂×C₃×C₅×D₄	—	2	1	no	—
84	C₂×C₃×C₅×D₄	—	2	1	no	—
85	C₂×C₃×C₅×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	—	4	1	no	—
87	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
88	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	—	2	1	no	—
91	C₂²×C₃×C₄×C₅	—	2	1	no	—
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₃×C₅×Q₁₆	—	4	1	no	—
95	C₃×C₅×SD₁₆	—	2	2	no	—
96	C₃×C₅×SD₁₆	—	4	1	no	—
97	C₃×C₅×M₁₆	—	4	1	no	—
98	C₂×C₃×C₅×C₈	—	4	1	no	—
99	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₃×C₅×C₄⋊C₄	—	2	1	no	—
104	C₃×C₅×C₄⋊C₄	—	2	1	no	—
105	C₃×C₅×C₄⋊C₄	—	2	1	no	—
106	C₃×C₅×C₄⋊C₄	—	2	1	no	—
107	C₃×C₅×C₄⋊C₄	—	2	1	no	—
108	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
109	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
116	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
117	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
120	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
121	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
122	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
123	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
124	C₃×C₄²×C₅	—	2	1	no	—
125	C₃×C₄²×C₅	—	2	1	no	—
126	C₃×C₄²×C₅	—	2	1	no	—
127	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
128	C₃×#556	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#546	C₂×C₅	1	1	yes	characteristic
130	C₃×#489	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#485	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#482	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#470	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#465	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#464	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#440	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#418	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#416	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
144	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
146	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
149	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
151	C₅×#126	—	2	1	no	—
152	C₅×#126	—	2	1	no	—
153	C₅×#124	—	2	1	no	—
154	C₅×#124	C₂²×C₃	1	1	yes	characteristic
155	C₅×#123	—	2	1	no	—
156	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
157	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
159	C₅×#121	—	2	1	no	—
160	C₅×#121	C₂²×C₃	1	1	yes	characteristic
161	C₅×#120	—	2	1	no	—
162	C₄×C₅×Q₈	—	2	1	no	—
163	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
165	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
166	C₅×#117	C₂²×C₃	1	1	yes	characteristic
167	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
169	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₅×#102	C₂²×C₃	1	1	yes	characteristic
178	C₅×#102	C₂²×C₃	1	1	yes	characteristic
179	C₅×#102	C₂²×C₃	1	1	yes	characteristic
180	C₅×#102	C₂²×C₃	1	1	yes	characteristic
181	C₅×#102	C₂²×C₃	1	1	yes	characteristic
182	C₅×#102	C₂²×C₃	1	1	yes	characteristic
183	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
186	#3311	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³×C₃×C₅	—	2	1	no	—
188	C₂³×C₃×C₅	—	2	1	no	—
189	C₂³×C₃×C₅	—	4	2	no	—
190	C₂³×C₃×C₅	—	4	2	no	—
191	C₂³×C₃×C₅	—	8	1	no	—
192	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
194	C₃×C₅×Q₈	—	2	1	no	—
195	C₃×C₅×Q₈	—	2	1	no	—
196	C₃×C₅×Q₈	—	2	1	no	—
197	C₃×C₅×Q₈	—	2	1	no	—
198	C₃×C₅×Q₈	—	4	2	no	—
199	C₃×C₅×D₄	—	2	1	no	—
200	C₃×C₅×D₄	—	2	1	no	—
201	C₃×C₅×D₄	—	2	1	no	—
202	C₃×C₅×D₄	—	4	1	no	—
203	C₃×C₅×D₄	—	4	2	no	—
204	C₃×C₅×D₄	—	4	2	no	—
205	C₃×C₅×D₄	—	8	1	no	—
206	C₃×C₅×D₄	#41	1	2	yes	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	4	2	no	—
218	C₂×C₃×C₄×C₅	—	8	1	no	—
219	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
220	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
221	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
222	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
223	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
224	C₃×C₅×C₈	—	2	1	no	—
225	C₃×C₅×C₈	—	2	1	no	—
226	C₃×C₅×C₈	—	2	1	no	—
227	C₃×C₅×C₈	—	2	1	no	—
228	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
229	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
231	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
234	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
235	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
236	C₃×#126	—	2	1	no	—
237	C₃×#126	—	2	1	no	—
238	C₃×#124	—	2	1	no	—
239	C₃×#124	C₂²×C₅	1	1	yes	characteristic
240	C₃×#123	—	2	1	no	—
241	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
242	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
243	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
244	C₃×#121	—	2	1	no	—
245	C₃×#121	C₂²×C₅	1	1	yes	characteristic
246	C₃×#120	—	2	1	no	—
247	C₃×C₄×Q₈	—	2	1	no	—
248	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
250	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
251	C₃×#117	C₂²×C₅	1	1	yes	characteristic
252	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
254	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
258	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
259	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₃×#102	C₂²×C₅	1	1	yes	characteristic
263	C₃×#102	C₂²×C₅	1	1	yes	characteristic
264	C₃×#102	C₂²×C₅	1	1	yes	characteristic
265	C₃×#102	C₂²×C₅	1	1	yes	characteristic
266	C₃×#102	C₂²×C₅	1	1	yes	characteristic
267	C₃×#102	C₂²×C₅	1	1	yes	characteristic
268	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
269	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂⁴×C₅	—	2	1	no	—
272	C₅×#41	—	2	2	no	—
273	C₅×#41	—	4	1	no	—
274	C₂×C₅×Q₈	—	2	1	no	—
275	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₅×D₄	—	2	2	no	—
278	C₂×C₅×D₄	—	2	1	no	—
279	C₂×C₅×D₄	—	2	1	no	—
280	C₂×C₅×D₄	—	2	1	no	—
281	C₂×C₅×D₄	—	4	1	no	—
282	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
283	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
284	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
285	C₂²×C₄×C₅	—	2	1	no	—
286	C₂²×C₄×C₅	—	2	1	no	—
287	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
289	C₅×Q₁₆	—	4	1	no	—
290	C₅×SD₁₆	—	2	2	no	—
291	C₅×SD₁₆	—	4	1	no	—
292	C₅×M₁₆	—	4	1	no	—
293	C₂×C₅×C₈	—	4	1	no	—
294	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
295	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
296	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
298	C₅×C₄⋊C₄	—	2	1	no	—
299	C₅×C₄⋊C₄	—	2	1	no	—
300	C₅×C₄⋊C₄	—	2	1	no	—
301	C₅×C₄⋊C₄	—	2	1	no	—
302	C₅×C₄⋊C₄	—	2	1	no	—
303	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
304	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
305	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
306	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
307	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
308	C₅×C₂²⋊C₄	—	2	1	no	—
309	C₅×C₂²⋊C₄	—	2	1	no	—
310	C₅×C₂²⋊C₄	—	2	1	no	—
311	C₅×C₂²⋊C₄	—	2	1	no	—
312	C₅×C₂²⋊C₄	—	2	1	no	—
313	C₅×C₂²⋊C₄	—	2	1	no	—
314	C₅×C₂²⋊C₄	—	2	1	no	—
315	C₅×C₂²⋊C₄	—	2	1	no	—
316	C₅×C₂²⋊C₄	—	2	1	no	—
317	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
318	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
319	C₄²×C₅	—	2	1	no	—
320	C₄²×C₅	—	2	1	no	—
321	C₄²×C₅	—	2	1	no	—
322	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
323	#556	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	#546	C₂×C₃×C₅	1	1	yes	characteristic
325	#489	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	#485	C₂×C₃×C₅	1	1	yes	characteristic, complemented
327	#482	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	#470	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	#464	C₂×C₃×C₅	1	1	yes	characteristic, complemented
332	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#418	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	#416	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	C₂²×C₃×C₅	—	2	1	no	—
339	C₂²×C₃×C₅	—	2	1	no	—
340	C₂²×C₃×C₅	—	2	2	no	—
341	C₂²×C₃×C₅	—	2	1	no	—
342	C₂²×C₃×C₅	—	2	1	no	—
343	C₂²×C₃×C₅	—	2	1	no	—
344	C₂²×C₃×C₅	—	2	1	no	—
345	C₂²×C₃×C₅	—	4	1	no	—
346	C₂²×C₃×C₅	—	4	1	no	—
347	C₂²×C₃×C₅	—	4	1	no	—
348	C₂²×C₃×C₅	—	4	1	no	—
349	C₂²×C₃×C₅	—	4	1	no	—
350	C₂²×C₃×C₅	—	8	4	no	—
351	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
352	C₃×C₄×C₅	—	2	1	no	—
353	C₃×C₄×C₅	—	2	1	no	—
354	C₃×C₄×C₅	—	2	1	no	—
355	C₃×C₄×C₅	—	2	1	no	—
356	C₃×C₄×C₅	—	4	1	no	—
357	C₃×C₄×C₅	—	4	1	no	—
358	C₃×C₄×C₅	—	4	1	no	—
359	C₃×C₄×C₅	—	4	1	no	—
360	C₃×C₄×C₅	—	4	1	no	—
361	C₃×C₄×C₅	—	4	1	no	—
362	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
363	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
364	C₂⁴×C₃	—	2	1	no	—
365	C₃×#41	—	2	2	no	—
366	C₃×#41	—	4	1	no	—
367	C₂×C₃×Q₈	—	2	1	no	—
368	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
369	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
370	C₂×C₃×D₄	—	2	2	no	—
371	C₂×C₃×D₄	—	2	1	no	—
372	C₂×C₃×D₄	—	2	1	no	—
373	C₂×C₃×D₄	—	2	1	no	—
374	C₂×C₃×D₄	—	4	1	no	—
375	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
376	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
378	C₂²×C₃×C₄	—	2	1	no	—
379	C₂²×C₃×C₄	—	2	1	no	—
380	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
382	C₃×Q₁₆	—	4	1	no	—
383	C₃×SD₁₆	—	2	2	no	—
384	C₃×SD₁₆	—	4	1	no	—
385	C₃×M₁₆	—	4	1	no	—
386	C₂×C₃×C₈	—	4	1	no	—
387	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
391	C₃×C₄⋊C₄	—	2	1	no	—
392	C₃×C₄⋊C₄	—	2	1	no	—
393	C₃×C₄⋊C₄	—	2	1	no	—
394	C₃×C₄⋊C₄	—	2	1	no	—
395	C₃×C₄⋊C₄	—	2	1	no	—
396	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
397	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
398	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
399	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
400	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
401	C₃×C₂²⋊C₄	—	2	1	no	—
402	C₃×C₂²⋊C₄	—	2	1	no	—
403	C₃×C₂²⋊C₄	—	2	1	no	—
404	C₃×C₂²⋊C₄	—	2	1	no	—
405	C₃×C₂²⋊C₄	—	2	1	no	—
406	C₃×C₂²⋊C₄	—	2	1	no	—
407	C₃×C₂²⋊C₄	—	2	1	no	—
408	C₃×C₂²⋊C₄	—	2	1	no	—
409	C₃×C₂²⋊C₄	—	2	1	no	—
410	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
411	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
412	C₃×C₄²	—	2	1	no	—
413	C₃×C₄²	—	2	1	no	—
414	C₃×C₄²	—	2	1	no	—
415	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
416	C₂³×C₅	—	2	1	no	—
417	C₂³×C₅	—	2	1	no	—
418	C₂³×C₅	—	4	2	no	—
419	C₂³×C₅	—	4	2	no	—
420	C₂³×C₅	—	8	1	no	—
421	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
422	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
423	C₅×Q₈	—	2	1	no	—
424	C₅×Q₈	—	2	1	no	—
425	C₅×Q₈	—	2	1	no	—
426	C₅×Q₈	—	2	1	no	—
427	C₅×Q₈	—	4	2	no	—
428	C₅×D₄	—	2	1	no	—
429	C₅×D₄	—	2	1	no	—
430	C₅×D₄	—	2	1	no	—
431	C₅×D₄	—	4	1	no	—
432	C₅×D₄	—	4	2	no	—
433	C₅×D₄	—	4	2	no	—
434	C₅×D₄	—	8	1	no	—
435	C₅×D₄	C₃×#41	1	2	yes	—
436	C₂×C₄×C₅	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
438	C₂×C₄×C₅	—	2	1	no	—
439	C₂×C₄×C₅	—	2	1	no	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	2	1	no	—
445	C₂×C₄×C₅	—	2	1	no	—
446	C₂×C₄×C₅	—	4	2	no	—
447	C₂×C₄×C₅	—	8	1	no	—
448	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
449	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
450	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
451	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
452	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
453	C₅×C₈	—	2	1	no	—
454	C₅×C₈	—	2	1	no	—
455	C₅×C₈	—	2	1	no	—
456	C₅×C₈	—	2	1	no	—
457	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
458	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
459	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
460	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
461	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
462	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
464	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
465	#126	—	2	1	no	—
466	#126	—	2	1	no	—
467	#124	—	2	1	no	—
468	#124	C₂²×C₃×C₅	1	1	yes	characteristic
469	#123	—	2	1	no	—
470	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
471	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
472	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
473	#121	—	2	1	no	—
474	#121	C₂²×C₃×C₅	1	1	yes	characteristic
475	#120	—	2	1	no	—
476	C₄×Q₈	—	2	1	no	—
477	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
478	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
479	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
480	#117	C₂²×C₃×C₅	1	1	yes	characteristic
481	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
484	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
485	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
486	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
487	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
488	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
489	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
490	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
491	#102	C₂²×C₃×C₅	1	1	yes	characteristic
492	#102	C₂²×C₃×C₅	1	1	yes	characteristic
493	#102	C₂²×C₃×C₅	1	1	yes	characteristic
494	#102	C₂²×C₃×C₅	1	1	yes	characteristic
495	#102	C₂²×C₃×C₅	1	1	yes	characteristic
496	#102	C₂²×C₃×C₅	1	1	yes	characteristic
497	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
498	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
499	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
500	C₂×C₃×C₅	—	4	1	no	—
501	C₂×C₃×C₅	—	4	1	no	—
502	C₂×C₃×C₅	—	4	2	no	—
503	C₂×C₃×C₅	—	8	1	no	—
504	C₂×C₃×C₅	#546	1	1	yes	characteristic
505	C₂×C₃×C₅	#575	1	1	yes	characteristic
506	C₂×C₃×C₅	#577	1	1	yes	characteristic
507	C₂³×C₃	—	2	1	no	—
508	C₂³×C₃	—	2	1	no	—
509	C₂³×C₃	—	4	2	no	—
510	C₂³×C₃	—	4	2	no	—
511	C₂³×C₃	—	8	1	no	—
512	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
513	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
514	C₃×Q₈	—	2	1	no	—
515	C₃×Q₈	—	2	1	no	—
516	C₃×Q₈	—	2	1	no	—
517	C₃×Q₈	—	2	1	no	—
518	C₃×Q₈	—	4	2	no	—
519	C₃×D₄	—	2	1	no	—
520	C₃×D₄	—	2	1	no	—
521	C₃×D₄	—	2	1	no	—
522	C₃×D₄	—	4	1	no	—
523	C₃×D₄	—	4	2	no	—
524	C₃×D₄	—	4	2	no	—
525	C₃×D₄	—	8	1	no	—
526	C₃×D₄	C₅×#41	1	2	yes	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	2	1	no	—
531	C₂×C₃×C₄	—	2	1	no	—
532	C₂×C₃×C₄	—	2	1	no	—
533	C₂×C₃×C₄	—	2	1	no	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	2	1	no	—
537	C₂×C₃×C₄	—	4	2	no	—
538	C₂×C₃×C₄	—	8	1	no	—
539	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
540	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
542	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
543	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
544	C₃×C₈	—	2	1	no	—
545	C₃×C₈	—	2	1	no	—
546	C₃×C₈	—	2	1	no	—
547	C₃×C₈	—	2	1	no	—
548	C₂²×C₅	—	2	1	no	—
549	C₂²×C₅	—	2	1	no	—
550	C₂²×C₅	—	2	1	no	—
551	C₂²×C₅	—	2	1	no	—
552	C₂²×C₅	—	2	1	no	—
553	C₂²×C₅	—	2	1	no	—
554	C₂²×C₅	—	2	2	no	—
555	C₂²×C₅	—	4	1	no	—
556	C₂²×C₅	—	4	1	no	—
557	C₂²×C₅	—	4	1	no	—
558	C₂²×C₅	—	4	1	no	—
559	C₂²×C₅	—	4	1	no	—
560	C₂²×C₅	—	8	4	no	—
561	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
562	C₄×C₅	—	2	1	no	—
563	C₄×C₅	—	2	1	no	—
564	C₄×C₅	—	2	1	no	—
565	C₄×C₅	—	2	1	no	—
566	C₄×C₅	—	4	1	no	—
567	C₄×C₅	—	4	1	no	—
568	C₄×C₅	—	4	1	no	—
569	C₄×C₅	—	4	1	no	—
570	C₄×C₅	—	4	1	no	—
571	C₄×C₅	—	4	1	no	—
572	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
573	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
574	C₂⁴	—	2	1	no	—
575	#41	—	2	2	no	—
576	#41	—	4	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
579	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	4	1	no	—
585	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
586	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
587	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
591	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
592	Q₁₆	—	4	1	no	—
593	SD₁₆	—	2	2	no	—
594	SD₁₆	—	4	1	no	—
595	M₁₆	—	4	1	no	—
596	C₂×C₈	—	4	1	no	—
597	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
598	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
599	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
600	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
607	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
608	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
609	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
610	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	2	1	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	2	1	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
621	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
626	C₃×C₅	#3311	1	1	yes	characteristic, direct product factor, Hall
627	C₂²×C₃	—	2	1	no	—
628	C₂²×C₃	—	2	1	no	—
629	C₂²×C₃	—	2	2	no	—
630	C₂²×C₃	—	2	1	no	—
631	C₂²×C₃	—	2	1	no	—
632	C₂²×C₃	—	2	1	no	—
633	C₂²×C₃	—	2	1	no	—
634	C₂²×C₃	—	4	1	no	—
635	C₂²×C₃	—	4	1	no	—
636	C₂²×C₃	—	4	1	no	—
637	C₂²×C₃	—	4	1	no	—
638	C₂²×C₃	—	4	1	no	—
639	C₂²×C₃	—	8	4	no	—
640	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
641	C₃×C₄	—	2	1	no	—
642	C₃×C₄	—	2	1	no	—
643	C₃×C₄	—	2	1	no	—
644	C₃×C₄	—	2	1	no	—
645	C₃×C₄	—	4	1	no	—
646	C₃×C₄	—	4	1	no	—
647	C₃×C₄	—	4	1	no	—
648	C₃×C₄	—	4	1	no	—
649	C₃×C₄	—	4	1	no	—
650	C₃×C₄	—	4	1	no	—
651	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
652	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
653	C₂×C₅	—	4	1	no	—
654	C₂×C₅	—	4	1	no	—
655	C₂×C₅	—	4	2	no	—
656	C₂×C₅	—	8	1	no	—
657	C₂×C₅	C₃×#546	1	1	yes	characteristic
658	C₂×C₅	C₃×#575	1	1	yes	characteristic
659	C₂×C₅	C₃×#577	1	1	yes	characteristic
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	8	1	no	—
665	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
666	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
667	Q₈	—	2	1	no	—
668	Q₈	—	2	1	no	—
669	Q₈	—	2	1	no	—
670	Q₈	—	2	1	no	—
671	Q₈	—	4	2	no	—
672	D₄	—	2	1	no	—
673	D₄	—	2	1	no	—
674	D₄	—	2	1	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	2	no	—
677	D₄	—	4	2	no	—
678	D₄	—	8	1	no	—
679	D₄	C₃×C₅×#41	1	2	yes	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	8	1	no	—
692	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
693	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
694	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
695	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
696	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
697	C₈	—	2	1	no	—
698	C₈	—	2	1	no	—
699	C₈	—	2	1	no	—
700	C₈	—	2	1	no	—
701	C₂×C₃	—	4	1	no	—
702	C₂×C₃	—	4	1	no	—
703	C₂×C₃	—	4	2	no	—
704	C₂×C₃	—	8	1	no	—
705	C₂×C₃	C₅×#546	1	1	yes	characteristic
706	C₂×C₃	C₅×#575	1	1	yes	characteristic
707	C₂×C₃	C₅×#577	1	1	yes	characteristic
708	C₅	C₃×#3311	1	1	yes	characteristic, direct product factor, Sylow
709	C₂²	—	2	1	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	8	4	no	—
722	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
723	C₄	—	2	1	no	—
724	C₄	—	2	1	no	—
725	C₄	—	2	1	no	—
726	C₄	—	2	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
734	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
735	C₃	C₅×#3311	1	1	yes	characteristic, direct product factor, Sylow
736	C₂	—	4	1	no	—
737	C₂	—	4	1	no	—
738	C₂	—	4	2	no	—
739	C₂	—	8	1	no	—
740	C₂	C₃×C₅×#546	1	1	yes	characteristic
741	C₂	C₃×C₅×#575	1	1	yes	characteristic
742	C₂	C₃×C₅×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#546	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₅×#556	C₂	semidirect
3. C₃×C₅×#489	C₂	semidirect
4. C₃×C₅×#485	C₂	semidirect
5. C₃×C₅×#482	C₂	semidirect
6. C₃×C₅×#476	C₂	semidirect
7. C₃×C₅×#470	C₂	semidirect
8. C₃×C₅×#465	C₂	semidirect
9. C₃×C₅×#464	C₂	semidirect
10. C₃×C₅×#452	C₂	semidirect
11. C₃×C₅×#450	C₂	semidirect
12. C₃×C₅×#440	C₂	semidirect
13. C₃×C₅×#435	C₂	semidirect
14. C₃×C₅×#418	C₂	semidirect
15. C₃×C₅×#416	C₂	semidirect
16. C₅×#3311	C₃	direct (N × H)
19. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
23. C₂²×C₃×C₅×C₈	C₂²	semidirect
24. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
32. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₄×C₅×Q₈	C₂²	semidirect
41. C₃×C₅×#117	C₂²	semidirect
43. C₃×C₅×#107	C₂²	semidirect
44. C₃×C₅×#106	C₂²	semidirect
45. C₃×C₅×#106	C₂²	semidirect
46. C₃×C₅×C₄⋊C₈	C₂²	semidirect
47. C₃×C₅×#103	C₂²	semidirect
48. C₃×C₅×#103	C₂²	semidirect
49. C₃×C₅×#103	C₂²	semidirect
50. C₃×C₅×#103	C₂²	semidirect
58. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
59. C₃×C₅×#97	C₂²	semidirect
60. C₃×#3311	C₅	direct (N × H)
61. C₅×#556	C₂×C₃	semidirect
63. C₅×#489	C₂×C₃	semidirect
64. C₅×#485	C₂×C₃	semidirect
65. C₅×#482	C₂×C₃	semidirect
66. C₅×#476	C₂×C₃	semidirect
67. C₅×#470	C₂×C₃	semidirect
68. C₅×#465	C₂×C₃	semidirect
69. C₅×#464	C₂×C₃	semidirect
70. C₅×#452	C₂×C₃	semidirect
71. C₅×#450	C₂×C₃	semidirect
72. C₅×#440	C₂×C₃	semidirect
73. C₅×#435	C₂×C₃	semidirect
74. C₅×#418	C₂×C₃	semidirect
75. C₅×#416	C₂×C₃	semidirect
128. C₃×#556	C₂×C₅	semidirect
130. C₃×#489	C₂×C₅	semidirect
131. C₃×#485	C₂×C₅	semidirect
132. C₃×#482	C₂×C₅	semidirect
133. C₃×#476	C₂×C₅	semidirect
134. C₃×#470	C₂×C₅	semidirect
135. C₃×#465	C₂×C₅	semidirect
136. C₃×#464	C₂×C₅	semidirect
137. C₃×#452	C₂×C₅	semidirect
138. C₃×#450	C₂×C₅	semidirect
139. C₃×#440	C₂×C₅	semidirect
140. C₃×#435	C₂×C₅	semidirect
141. C₃×#418	C₂×C₅	semidirect
142. C₃×#416	C₂×C₅	semidirect
145. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
149. C₂²×C₅×C₈	C₂²×C₃	semidirect
150. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
158. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
163. C₄×C₅×Q₈	C₂²×C₃	semidirect
167. C₅×#117	C₂²×C₃	semidirect
169. C₅×#107	C₂²×C₃	semidirect
170. C₅×#106	C₂²×C₃	semidirect
171. C₅×#106	C₂²×C₃	semidirect
172. C₅×C₄⋊C₈	C₂²×C₃	semidirect
173. C₅×#103	C₂²×C₃	semidirect
174. C₅×#103	C₂²×C₃	semidirect
175. C₅×#103	C₂²×C₃	semidirect
176. C₅×#103	C₂²×C₃	semidirect
184. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
185. C₅×#97	C₂²×C₃	semidirect
186. #3311	C₃×C₅	direct (N × H)
230. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
234. C₂²×C₃×C₈	C₂²×C₅	semidirect
235. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
243. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
248. C₃×C₄×Q₈	C₂²×C₅	semidirect
252. C₃×#117	C₂²×C₅	semidirect
254. C₃×#107	C₂²×C₅	semidirect
255. C₃×#106	C₂²×C₅	semidirect
256. C₃×#106	C₂²×C₅	semidirect
257. C₃×C₄⋊C₈	C₂²×C₅	semidirect
258. C₃×#103	C₂²×C₅	semidirect
259. C₃×#103	C₂²×C₅	semidirect
260. C₃×#103	C₂²×C₅	semidirect
261. C₃×#103	C₂²×C₅	semidirect
269. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
270. C₃×#97	C₂²×C₅	semidirect
323. #556	C₂×C₃×C₅	semidirect
325. #489	C₂×C₃×C₅	semidirect
326. #485	C₂×C₃×C₅	semidirect
327. #482	C₂×C₃×C₅	semidirect
328. #476	C₂×C₃×C₅	semidirect
329. #470	C₂×C₃×C₅	semidirect
330. #465	C₂×C₃×C₅	semidirect
331. #464	C₂×C₃×C₅	semidirect
332. #452	C₂×C₃×C₅	semidirect
333. #450	C₂×C₃×C₅	semidirect
334. #440	C₂×C₃×C₅	semidirect
335. #435	C₂×C₃×C₅	semidirect
336. #418	C₂×C₃×C₅	semidirect
337. #416	C₂×C₃×C₅	semidirect
459. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
463. C₂²×C₈	C₂²×C₃×C₅	semidirect
464. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
472. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
477. C₄×Q₈	C₂²×C₃×C₅	semidirect
481. #117	C₂²×C₃×C₅	semidirect
483. #107	C₂²×C₃×C₅	semidirect
484. #106	C₂²×C₃×C₅	semidirect
485. #106	C₂²×C₃×C₅	semidirect
486. C₄⋊C₈	C₂²×C₃×C₅	semidirect
487. #103	C₂²×C₃×C₅	semidirect
488. #103	C₂²×C₃×C₅	semidirect
489. #103	C₂²×C₃×C₅	semidirect
490. #103	C₂²×C₃×C₅	semidirect
498. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
499. #97	C₂²×C₃×C₅	semidirect
626. C₃×C₅	#3311	direct (N × H)
708. C₅	C₃×#3311	direct (N × H)
735. C₃	C₅×#3311	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#556	2
C₃×C₅×#546	2
C₃×C₅×#489	2
C₃×C₅×#485	2
C₃×C₅×#482	2
C₃×C₅×#476	2
C₃×C₅×#470	2
C₃×C₅×#465	2
C₃×C₅×#464	2
C₃×C₅×#452	2
C₃×C₅×#450	2
C₃×C₅×#440	2
C₃×C₅×#435	2
C₃×C₅×#418	2
C₃×C₅×#416	2
C₅×#3311	3
C₃×#3311	5

Subgroups — C3×C5×#3311 #14276345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3311 #14276345